Quantum Reprogramming - A Long Overdue and Least Intrusive Reality Adaptation of the Copenhagen Interpretation
| Scientific Paper | |
|---|---|
| Title | Quantum Reprogramming - A Long Overdue and Least Intrusive Reality Adaptation of the Copenhagen Interpretation |
| Read in full | Link to paper |
| Author(s) | Evert Jan Post |
| Keywords | Copenhagen, quantum mechanics, Quantum Theory |
| Published | 2005 |
| Journal | Annales de la Fondation Louis de Broglie |
| Volume | 30 |
| Number | 3-4 |
| No. of pages | 18 |
Read the full paper here
Abstract
This essay is an unapologetic proposal for incisive changes in the traditional Copenhagen interpretation of quantum mechanics. Instead of a single system, the Schroedinger Ψ describes an ensemble of identical systems obeying a classical statistics. Since the Schroedinger equation is now to be taken as solely describing randomized ensembles, it can no longer be regarded, and should no longer be used, as a method of primary quantization such as might be associated with single systems. The variational argument used by Schroedinger for obtaining his equation now graduates to a derivation from pre-1925 propositions of quantization. Following Kiehn [9], pre-1925 quantizations are recognized as part of a mathematical system of period (residue) integrals describing global topological structure of single systems. Since these single system tools operate in a pre-statistical realm, it follows Heisenberg uncertainty, which derives from Schroedinger's equation, now conveys limitations of observation associated with ensemble randomness. Following Planck, this randomness is maintained by the zero-point energy. For mathematical details of these conceptual alternatives the reader is referred to ref.5.
Overview
Evert Jan Post's essay makes one change to the Copenhagen interpretation and follows its consequences. The change is that Schrödinger's Ψ describes a real ensemble of identical systems obeying ordinary classical statistics, not a single system. Post calls this "least intrusive" deliberately: nothing in the working formalism is altered, no hidden variables are added, and essentially every past application survives. What is removed is the doctrine that Ψ is the primary description of an individual system, and with it the "nonclassical" character that doctrine forced on quantum statistics.
The consequences are large. If the Schrödinger equation is an ensemble tool, it cannot be the method of primary quantization; the pre-1925 quantization conditions cease to be crude approximations superseded by wave mechanics and become the single-system laws, expressed as period or residue integrals describing global topological structure. Heisenberg uncertainty, being derivable from the Schrödinger equation (as Kennard showed), then expresses limitations of observation on a randomized ensemble rather than an absolute limit on knowledge of an individual system. The result is a two-tier scheme: a pre-statistical tier of single systems governed by period integrals, and a statistical tier of randomized ensembles governed by Schrödinger and Dirac.
The argument
How the single-system reading took hold
Post sets the scene historically. Courant-Hilbert's treatise had just appeared, seemingly "made to measure" for the quantum pioneers, and its eigenvalue techniques — originally about resonances of macroscopic musical instruments — were carried over to atoms and molecules. This began "an era of wave-monism, suggesting everything is waves, a sentiment still quite prevalent today." Max Born's reading of Ψ as a probability amplitude, "like a square root of a probability density," was instrumental in what followed.
His diagnosis of the resulting error is a point about statistics rather than about physics. Normal statistics compares a state of disorder against a reference state of order. Copenhagen accepted a priori disorder with no state of order to compare with, and, needing a name for a statistics without such a reference, called it nonclassical. Post: "This word became a fateful step in determining in what light much of quantum physics would be perceived in the next three quarters of a century. Questions how we recognize disorder, without a reference state of order, had not yet become part of a more incisive concern of that time."
Planck's 1912 zero-point energy
The essay's central piece of evidence is a priority claim. In 1912, well before the Schrödinger equation existed, Max Planck had already obtained the residue hν/2 per harmonic oscillator — not as an axiom but as "a minimal condition for (finite) ensembles to retain a state of optimal phase disorder."
Post then presses the difference. Copenhagen assigned hν/2 to every harmonic oscillator as a permanent attribute. But Rayleigh, Jeans and Planck had shown that any finite domain of free space accommodates an infinity of electromagnetic oscillators, so the assignment refills space with infinite energy — the very ultraviolet catastrophe Planck's quantum hypothesis had removed. His verdict on the two calculations is the essay's sharpest formulation: "Planck's calculation gives the how and why of zero-point energy, whereas the Schroedinger equation only gives the how not the why."
He presses the consequence rhetorically as well: while Quantum Electrodynamics has "made into a fine art" the balancing of infinities, astronomers complain of too little mass to hold structures together. "Are the QED people and astronomers on speaking terms? Have they heard of E = Mc2? If E is infinite wouldn't M be too?"
Corroborating evidence
Post adds a second classical counter-example, drawn from the Feynman Lectures: a perfectly classical statistical calculation of the average modulus of angular momentum √[n(n+1)]ħ for an ensemble of orientation-randomized rotators. The authors present it in Volumes II and III without identifying it as a counter-example to nonclassical statistics — "perhaps tongue in cheek, a challenge to the physics establishment." Post suspects Richard Feynman and his co-authors were simply unaware of Planck's 1912 result, since "had they known, one would have thought Feynman had the kind of personality that would have led to a confrontation right there and then."
He identifies the two statistical parameters that were overlooked as mutual phase and orientation of ensemble elements, and draws a striking conclusion about hidden variables: "David Bohm's hidden variables were not hidden to Max Planck." The ensemble reading was proposed by Popper to Einstein in 1934; Einstein criticized it, but a footnote on the first page of his reply explicitly acknowledges an aggregate connotation for Ψ. Post's complaint about the ensemble minority that did emerge is that it "bought wholesale into Copenhagen's premise of a non-classical statistics," so both camps continued to grant primary status to the Schrödinger-Dirac equations and "prejudicially denied a conceivable existence of separate pre-statistical single system laws."
The pre-statistical tier: period integrals
Post's positive proposal, following Kiehn and the cohomology of de Rham, is that the single-system laws are cyclic (period, or residue) integrals, which count things and therefore need no metric. The Aharonov-Bohm integral becomes "a counter of entities known as flux quanta." Since counting identical quanta must be independent of metric and reference specification, the law meets the premises of general relativity automatically — which, Post argues, "removes an old conceptual barrier between quantum theory and relativity." It also explains why covariant transcriptions of the Dirac equation failed to give meaningful results: "ensemble-based tools are not well suited for isolating ensemble-independent features of physical law."
The logical order is thereby inverted. The Aharonov-Bohm integral is currently viewed as Schrödinger-derived, and so inherits Copenhagen's limitations. On Post's reading, "it is Schroedinger's equation with its statistical base that is contingent on the pre-statistical Aharonov-Bohm integral, not the other way around," and Schrödinger's variational recipe becomes a generalized form of Planck's zero-point calculation — which upgrades the recipe to a genuine derivation. He cites the flux quantization experiments of Deaver-Fairbanks and Doll-Näbauer (1961) as direct confirmations of the pre-statistical Aharonov-Bohm law, notes the residues are h/e in applied fields and h/2e in self-fields, and places this integral alongside Gauss's law as a counter of charge quanta and Kiehn's product integral as a counter of action quanta.
The quantum Hall effect as test case
Post's most concrete complaint concerns the fractional quantum Hall effect. He had proposed in 1982 (Foundations of Physics 12, 169, at p. 194) a two-quantum-number description via period integrals, shortly before the first fractional reports appeared. The Schrödinger-based account was adopted instead, and in his view generated "an extravaganza of nonclassical propositions ranging from fractional charge to exotic new fermions underlining a presumed different nature of integer and fractional effect." Over two decades of papers, he says, not one besides his own compares the period-integral alternative; and when Mead's Collective Electrodynamics (2000) later gave a two-quantum-number account of both effects, it referred neither to the prevailing dichotomy nor to the earlier alternative. He is candid that the quantum Hall effect is his example of "silently sneaking in pre-statistic situations to be processed with statistical tools."
Sociology of the blockage
The closing pages are about why the revision has not been made. Post argues that overspecialization narrows the range of experience on which conscience operates: "The narrower the experience, the greater is the tendency of accepting miracles and getting on bandwagons to feel safe." Editors and reviewers were educated in an era that learned to live with nonclassical blind spots and feel duty-bound to defend them. "Reduced rational processing in physical theory has made this discipline more susceptible to seeking recourse in dogma when rational progress is not forthcoming." He recommends Mara Beller's Quantum Dialogue as reading on the point, and ends by inverting the usual complaint about mathematical overload: "More involvement with mathematical form can avoid much unsuitable mathematics."
Assessment
The essay's core historical claim is checkable and correct, and it is the most valuable thing in it: Planck's 1912 second theory of radiation does contain a zero-point residue hν/2 derived as a condition on phase-randomized ensembles, more than a decade before wave mechanics. That the same number arises from two routes with different logical status — one derived from an ensemble condition, one falling out of an equation whose interpretation is contested — is a real observation, and Post is right that it is almost never taught. The methodological point about statistics is also sound: a statistics of disorder with no reference state of order is an odd object, and naming it "nonclassical" did foreclose the question rather than answer it.
The positive programme is more attractive than its exposition. The observation that flux quantization, charge quantization and action quantization are all counting statements, and that counting is metric-independent and therefore automatically covariant, is a genuinely elegant reason to treat cyclic integrals as more fundamental than the wave equation. The ensemble interpretation itself is respectable and has serious adherents; nothing Post proposes conflicts with any measured quantum result, which is what he means by "least intrusive."
The difficulties are of two kinds. The first is that this essay asserts far more than it derives. Post repeatedly refers the reader elsewhere for the mathematics — to Volume 181 of the Boston Studies in the Philosophy of Science — so the crucial claims that Schrödinger's variational argument "graduates to a derivation" from period integrals, and that the fractional quantum Hall effect follows from a two-quantum-number period-integral account, cannot be assessed from what is on the page. The phrase "we have now established, and dare I say beyond a shadow of a doubt, that the Schroedinger equation is a tool applying to a real ensemble" is not supported by anything preceding it; what precedes it are two suggestive examples and a historical grievance.
The second is that the ensemble reading, taken alone, does not do everything Post needs. An ensemble interpretation without additional structure has to say something about individual outcomes, and it must accommodate the Bell-type correlations measured in the Aspect experiments and their successors, which constrain any account in which ensemble members carry definite pre-existing local properties. Post touches Bohm only to say his hidden variables "were not hidden to Max Planck," and does not engage the Bell results at all. Nor does he address single-system interference — the build-up of a two-slit pattern one particle at a time — which is precisely the experimental situation an ensemble-only reading of Ψ must explain rather than dismiss as an artefact of Copenhagen prejudice.
There is also an internal tension. Post argues that Heisenberg uncertainty is a consequence of ensemble randomness and therefore "can no longer be an absolute and always present manifestation," while also holding that the randomness is maintained by a zero-point energy that Planck derived as a minimal condition for finite ensembles. If the zero-point energy is always present, the randomness it maintains is too, and the practical difference from the Copenhagen limit becomes hard to locate. He gestures at "highly ordered physical situations" — quantum interferometry, the quantum Hall effect — as the place where the two tiers separate, but does not give a criterion for when a situation is ordered enough to be pre-statistical.
The final third, on editorial conservatism and overspecialization, is the weakest as argument and the most quotable. Post's citation record for the fractional quantum Hall effect may well be as he describes it, but neglect is not evidence of correctness, and the essay does not attempt to show that the period-integral account reproduces the observed fractions.